Answer:
Step-by-step explanation:
The answer is B because if you multiply 5 by 2 it equals 10.
The answer could also be D because if you multiply 3 by 2 it equals 6.
Simplify the expression by combining like terms
36a + 42b - 18a + 6
The simplified expression, 36a + 42b - 18a + 6 by combining the like terms is 18a + 42b + 6
How to simplify expression?In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.).
To simplify an expression means to write an equivalent expression which contains no similar terms.
Therefore, let's simplify the expression by combining the like terms.
36a + 42b - 18a + 6
Like terms can be defined as terms that contain the same variables raised to the same power.
36a + 42b - 18a + 6
combining the like terms
36a - 18a + 42b + 6
Therefore, the simplified expression is 18a + 42b + 6
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If 1/3 pound of pecans cost $2.25 what is the cost per pound for pecans
Answer:
$6.75 Per pound
Step-by-step explanation:
2.25 = 1/3
2.25 + 2.25 = 2/3
2.25 + 2.25 + 2.25 = 6.75 / 3/3
a young entrepreneur purchased a lemonade stand for $30 each cup of lemonade cost $0.25 in materials let x equal the number of lemonade cups sold which functions represents the average cost C, if a cup of lemonade ?
The cost of the lemonade stand is $ 30.
The number of lemonade cups is x.
The price of each cup of lemonade is $ 0.25.
The cost function can be determined as,
[tex]\begin{gathered} c(x)=average\cos t\text{ of lemonade stand}+\text{price of each cup} \\ =\frac{30}{x}+0.25 \\ =\frac{30+0.25x}{x} \end{gathered}[/tex]Thus, option (A) is the correct option.
3. Last year in January Nugget Park employed 520 workers. At the end of the
year 195 employees were made redundant. What fraction of the workforce
kept their jobs?
[tex]\frac{325}{520}[/tex] fraction of the workforce kept their jobs
What is the Percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
What is Percentage change?
The percentage increase is calculated by subtracting the original number from the new number, dividing that result by the original number, and multiplying that result by 100.
where growth in number equals new number minus initial number.
Similar to how a percentage increase is calculated, a percentage reduction is calculated by subtracting a new number from the original number, dividing that new number by the original number, and multiplying that result by 100.
decreasing number where original number - new number
In other words, there is a percentage decline if the response is negative.
Here, It is given:
In January 520 workers were employed;
In the end, 195 employees were redundant;
So, The fraction of the workforce who kept their job:-
The fraction of the workforce who kept their job=[tex]\frac{520-195}{520}[/tex]
The fraction of the workforce who kept their job=[tex]\frac{325}{520}[/tex]
Hence,
The fraction of the workforce who kept their job=[tex]\frac{325}{520}[/tex]
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help meeeeeeeeeeeeeee pleaseeeeeee
Answer: Width = 5.7 feet, Length = 10.5 feet
Step-by-step explanation:
Let the width be w. Then, the length is 2w-0.9.
[tex]w(2w-0.9)=59.85\\\\2w^2 -0.9w-59.85=0\\\\w =\frac{-(-0.9) \pm \sqrt{(-0.9)^2 -4(2)(-59.85)}}{2(2)}\\\\w =5.7\\\\\implies 2w-0.9=10.5[/tex]
Reduce the algebraic fraction. y^3-3y^2+y-3/y^2-9
The reduce algebraic fraction is [tex]\frac{y^2 + 1}{y + 3}[/tex]
What is algebraic fraction?Algebraic fraction are simply fractions with algebraic expressions on the top and/or bottom
We follow the step to reduce to algebraic fraction
[tex]\frac{y^3 - 3y^2 -3 }{y^2 - 9}[/tex]
Simplify the numerator
[tex]\frac{ (y - 3) )(y^2 + 1 )}{y^2 -9}[/tex]
Factor out the greatest common factor from each group
[tex]\frac{(y^3 -3y^2 ) = y -3}{y^2 - 9}[/tex]
Find out greatest common factor (GCF) from each group
[tex]\frac{y^2 (y + 3) + 1 (y - 3)}{y^2 - 9}[/tex]
Simplify the denominator and rewrite 9 as [tex]3^{2}[/tex]
[tex]\frac{( y - 3 ) (y^2 + 1 ) }{y^2 - 3^2}[/tex]
Since both terms are perfect squares, factor using the difference of squares formula
[tex]a^{2}- b^2 = (a +b ) (a -b)[/tex] where a = y and b = 3
[tex]\frac{( y - 3) (y^2 + 1 )}{(y + 3 ) (y -3)}[/tex]
Evaluate the equation and rewrite the expression
[tex]\frac{y^2 + 1}{y + 3}[/tex]
Therefore, the reduce algebraic fraction is [tex]\frac{y^2 + 1}{y + 3}[/tex]
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lucy uses 4 round beads and 5 cube head beads to make a special necklace. lucy bought one package of 56 triangular beads, one package of 30 round beads, six bananas, one package of 24 cube bead beads, and three fish sandwiches. she usually makes her necklaces in the living room, but today she plans to make them in her bedroom
The number of special necklaces that she can produce, using proportions, is obtained as follows:
4.
What is a proportion?A proportion represents a fraction relative to a total amount, which is combined with the basic arithmetic operations to find the desired amounts in whichever context of a problem.
The requirements for each special necklace are listed as follows, from the problem:
4 round beads.5 cube heads.The amounts purchased are given as follows:
30 round beads.24 cube beads.The amount of round beads purchased is enough for:
30/4 = 7.5 special necklaces.
The amount of cube beads purchased is enough for:
24/5 = 4.8 special necklaces.
Hence the number of special necklaces that she can make is of:
4.
Because:
The lower limit of the amounts is of 4.The amount is rounded down, as there would not be enough cube beads for the fifth necklace.Missing InformationThe complete problem is given by the image shown at the end of the answer.
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If
C
=
−
x
+
2
C=−x+2 and
D
=
x
2
+
8
x
−
1
,
D=x
2
+8x−1, find an expression that equals
3
C
+
3
D
3C+3D in standard form.
The expression that equals 3C+3D in standard form is:
x²+7x+1
Given:
C = -x+2
and D = x²+8x-1
we are asked to find out an expression which equals 3C+3D in standard form.
based on the conditions, formulate:
3C+3D
substitute C and D values.
⇒ 3(-x+2) + 3(x²+8x-1)
Apply multiplicative distribution law:
⇒ open the parenthesis.
⇒ -3x+6+3x²+24x-3
calculate the product or quotient
⇒ arrange the like terms.
⇒ 3x²+21x+3
⇒ Reduce the terms.
⇒ x²+7x+1
Hence we get the equation in standard form.
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Two and six-tenths times a number, x, plus 5 is y.
Answer:
2,6x +5 = y
Step-by-step explanation:
Don’t know if you wanted the equation, but this is how it’s written
If 200 copies are made for $6.00, then what is the unit rate price per copy? How much will 150 copies cost?
To calculate the unit race price per copy, we can divide $6.00 by 200 copies:
[tex]\frac{6}{200}=0.03\text{ usd}[/tex]Each copy cost $0.03, to determine how much will cost 150 copies, we have to multiply the unit rate price by 150:
[tex]0.03\cdot150=4.5\text{ usd}[/tex]150 copies will cost $4.5
Find the 54th term of the following arithmetic sequence.15, 22, 29, 36,...
Type the correct answer in the box. Rewrite the quadratic function in the form that best reveals the zeros of the function.
Answer:
f(x) = (2x + 3)(2x + 1)
Explanation:
The form that best reveals the zeros of the function is:
f(x) = (x - a)(x - b)
Where a and b are the zeros of the function.
So, we need to apply the distributive property as:
[tex]\begin{gathered} f(x)=2(2x^2+4x)+3 \\ f(x)=2\cdot2x^2+2\cdot4x+3 \\ f(x)=4x^2+8x+3 \end{gathered}[/tex]Then, we can factorize the quadratic function as:
[tex]f(x)=(2x+3)(2x+1)[/tex]So, now we can identify the zeros of the function if we solve the following equation:
[tex]\begin{gathered} f(x)=(2x+3)(2x+1)=0 \\ 2x+3=0\rightarrow x=-\frac{3}{2} \\ or \\ 2x+1=0\rightarrow x=-\frac{1}{2} \end{gathered}[/tex]Therefore, the form that best reveals the zeros in the function is:
f(x) = (2x + 3)(2x + 1)
The length of the base of an isosceles triangle is x. The length of a leg is 5x−4. The perimeter of the triangle is 102. Find x.
In the given isosceles triangle, the value of x is 10 units.
What is a triangle?A triangle is a polygon with three edges and three vertices. It belongs to the basic geometric shapes. A triangle having vertices A, B, and C is known as triangle ABC. Any three locations in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.So, the value of 'x' will be:
Given triangle is an isosceles triangle. Then,
x + 5x - 4 + 5x - 4 = 10211x - 8 = 10211x = 102 + 811x = 110x = 110/11x = 10Therefore, in the given isosceles triangle, the value of x is 10 units.
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Help my daughter needs to know how to do this she’s asking me I’m lost
Given:
[tex]\begin{gathered} V=L\times W\times H \\ V=64 \\ L=8 \\ H=4 \end{gathered}[/tex]Solve:
Put the all value then:
[tex]\begin{gathered} V=L\times W\times H \\ 64=8\times W\times4 \\ 64=32\times W \\ W=\frac{64}{32} \\ W=2 \end{gathered}[/tex]So the value of W is 2.
(e) Cards are 65p each and gift wrap
sheets are 45p each at a gift shop. Owen
buys 21 items from the shop and spends
£11.85. How many cards and how many
gift wrap sheets did Owen buy?
Owen bought 9 gift wrap sheets.
Given, Cards are 65p each and gift wrap sheets are 45p each at a gift shop.
Owen buys 21 items from the shop and spends £11.85.
Let the number of cards be x,
the number of gift wrap sheets be y
Now, according to question
x + y = 21
0.65x + 0.45y = 11.85
On multiplying the first equation by 0.45, we get
0.45x + 0.45y = 9.45
0.65x + 0.45y = 11.85
On subtracting, we get
0.2x = 2.4
x = 12
On solving, we get
12 + y = 21
y = 9
Hence, Owen bought 9 gift wrap sheets.
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Mr.Wells drew a plan for a rectangular dog run. The vertices are (2 1/3, 7 1/2), (12, 7 1/2),(12, 1) and (2 1/3, 1). What is the perimeter of the dog run?
Perimeter of rectangular dog run is 32.34 units.
Given,
Vertices of rectangular dog run are [tex](2\frac{1}{3},7\frac{1}{2} ), (12,7\frac{1}{2}), (12,1), (2\frac{1}{3},1 )[/tex]
Let
[tex]A=(2\frac{1}{3},7\frac{1}{2} )=(\frac{7}{3} , \frac{15}{2} } )\\ \\B=(12,7\frac{1}{2})=(12,\frac{15}{2} )\\\\ C=(12,1)\\ \\D=(2\frac{1}{3},1 )=(\frac{7}{3},1)[/tex]
A, B,C and D be the vertices of the rectangular dog run as shown in figure.
In rectangle opposite sides are equal. thus, AB=CD and BC=AD
In this rectangle, AB is length and BC is width.
To find distance of AB and BC use formula,
[tex]Distance=\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
[tex]AB=\sqrt{(12-\frac{7}{3} )^2+(\frac{15}{2}-\frac{15}{2} )^2} = \sqrt{(\frac{36-7}{3} )^2} =\frac{29}{3}= 9.67[/tex][tex]Bc=\sqrt{(12-12 )^2+(1-\frac{15}{2} )^2} = \sqrt{(\frac{2-15}{2} )^2} =\sqrt{(\frac{-13}{2})^2} = 6.5[/tex]
To find perimeter of rectangular dog run use formula,
[tex]Perimeter =2(Length + Width)\\\\Perimeter =2(AB+BC)\\\\Perimeter =2(9.67+6.5)\\\\Perimeter=2(16.17)\\\\Perimeter=32.34[/tex]
Hence, perimeter of rectangular dog run is 32.34 units.
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at a butcher shop, hilda bought 7 1/4 lb of beef she left with 18 9/20 lb of meat express the numbers of pounds of pork she bought using a decimal
Using mathematical operations, we can conclude that the pound of pork the girl brought was 11.2 pounds.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition Subtraction (from left to right).So, the pounds of pork the girl bought:
Beef bought: 7¼Total meat: 18 9/20Calculate pork as:
18 9/20 - 7¼369/20 - 29/4369 - 5(29)/20369 - 145/20224/2011.2Therefore, using mathematical operations, we can conclude that the pound of pork the girl brought was 11.2 pounds.
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If BD=3, then CD= [blank] −−−−−−.Enter your answer as the number that correctly fills in the blank.
From the information given,
BA is congruent to AC
AD is common to triangle ABD and ACD
Since the two sides of triangle ABC are congruent, it means that the triangle is an isosceles triangle. Thus,
angle ABD = angle ACD
Triangle ABD and ACD are congruent. Thus, the corresponding sides are congruent
If BD = 3, then
CD = 3
4 1/2 > 1.2x
X >3 3/4
X<3 3/34
X>5 2/5
X<5 2/5
Answer:
x>3 3/4
Step-by-step explanation:
you need to swap the sides and divide by 1.2
help meeeeeeeeee pleasee
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
The Matthews’ family paid $265,000 when they bought their house in 2005. It is now worth $319,000. What is the percent increase on the price of the home?
The percent increase on the price of the home is 20.37%.
What is percent increase?
A percent increase refers to how much a percentage has gone up over time. In order to reach this number, you would need to find the difference between the original value and the final value, subtracting to find the exact total of the decrease.
Formula is given by
New number (value) – original number (value) = increase
Increase / original number (value) x 100 = percent increase
Given ,
initial value of home = $265,000
After few years, the value = $319,000
Increase = $319,000 - 265,000
=54000
Percent increase = 54000/265000× 100
= 20.37%
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11. a $58 video game is on sale for a 14% discount. what is the price with the discount
As given by the question
There are given that the price of the video games is $58.
Now,
According to the question, there are given that 14% discount on their game price
So,
The price with discount is:
[tex]58\times\frac{14}{100}=8.12[/tex]Then,
[tex]58-8.12=49.88[/tex]Hence, the price with the discount is $49.88
What is a Unit Circle?
The "Unit Circle" is a circle with a radius of 1.
The center is put on a graph where the x axis and y axis cross, so we get this neat arrangement here.
The graph is given by:
Answer:
A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the functions of trigonometry are most simply defined using the unit circle.
Step-by-step explanation:
I need help please hellp asap now pleas
Find the equation of the line that passes through the point (-2, 7) and is parallel to the line y=4x+1. The answer must be written in the form ax+by+c=0, where a, b, c are integers
The equation of the line 4 · x - y + 15 = 0 is parallel to the line y = 4 · x + 1.
How to find the equation of the line parallel to another line
In this problem we must determine the equation of a line that is parallel to the line y = 4 · x + 1 and that passes through the point (x, y) = (- 2, 7). Lines are represented by algebraic equations of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.Two lines are parallel if both share the same slope.
First, find the slope of the first line:
m = 4
Second, determine the intercept of the parallel line:
b = y - m · x
b = 7 - 4 · (- 2)
b = 7 + 8
b = 15
Third, write the resulting expression and find its standard form:
y = 4 · x + 15
4 · x - y + 15 = 0
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If UV = 2x, VW = x + 4, and UW = 10, what is UV?
ANSWER:
4
STEP-BY-STEP EXPLANATION:
From a graph we can establish the following equation:
[tex]\begin{gathered} UV+VW=UW \\ \\ \text{ We replacing} \\ \\ 2x+x+4=10 \end{gathered}[/tex]We solve for x:
[tex]\begin{gathered} 3x+4=10 \\ \\ 3x=10-4 \\ \\ x=\frac{6}{3} \\ \\ x=2 \\ \\ \text{ Now, for UV} \\ \\ UV=2\cdot2 \\ \\ UV=4 \end{gathered}[/tex]The value of UV is equal to 4
Solve for X: 3. (7x - 1) 125 Submit Question
Answer:
From the given figure;
[tex](7x-1)^0=125^0[/tex]Reason: Alternate angle.
Solving for x;
[tex]\begin{gathered} 7x-1=125 \\ 7x=125+1 \\ 7x=126 \\ x=\frac{126}{7} \\ x=18 \end{gathered}[/tex]Therefore, the value of x is;
[tex]x=18[/tex]could you help me out
we can do a triangle to solve the apothem
the upper angle is equal to 360 divided by 8 since 360 is a complete turn and an octagon is composed of 8 equal triangles, so is 45
now we take a triangle from the triangle to apply trigonometric ratios and solve a
the upper angle of the new triangle is the half of the original so is 45/2
now i will use the trigonometric ratio of tangent
[tex]\tan (\alpha)=\frac{O}{A}[/tex]where alpha is the angle, O the opposite side drom the angle and a the adjacent side from the angle
so replacing
[tex]\tan (\frac{45}{2})=\frac{3.5}{a}[/tex]and solve for a
[tex]\begin{gathered} a=\frac{3.5}{\tan (\frac{45}{2})} \\ \\ a\approx8.4 \end{gathered}[/tex]the aphotem is 8.4
and the formula of the area of the octagon is
[tex]A=4\times a\times l[/tex]where a is the aphotem and l the measure f each side so 7
replacing
[tex]\begin{gathered} A=4\times8.4\times7 \\ A=235.2 \end{gathered}[/tex]the area is 235.2 square units
Eddie Munson can ship 52 chocolates in a hour so how long will it take for him to ship 65 chocolates
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 10.8 seconds
Step-by-step explanation:
[tex]-16t^2 +170t+40=10\\\\16t^2 -170t-30=0\\ \\ t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)[/tex]